The U.S. and Mexico are taking a first step toward solving the crisis on their shared border.

In a potential breakthrough that could staunch the flow of migrant caravans and untangle some of the nation’s most controversial immigration problems, Mexico’s incoming president has agreed to a Trump administration plan that will make Central American asylum seekers stay on the Mexican side of the border while they wait to be legally admitted to the United States.

The plan, called “Remain in Mexico,” was negotiated last week by Secretary of State Mike Pompeo, Homeland Security Secretary Kirstjen Nielsen and other US officials, the Washington Post reported Saturday.

They met in Houston with representatives of Mexican president-elect Andrés Manuel López Obrador, who takes power Dec. 1.

The program is meant to put a stop to the “catch-and-release” system, long denounced by Trump, that allows migrants seeking refuge in the United States to live here for years — a practice that immigration officials see as a dangerous loophole that encourages illegal border crossings and contributes to years-long backups in the adjudication system.

Mexico’s previous leaders have resisted American calls to halt the flow of Central American migrants through Mexican territory and have regarded the issue of illegal immigration through the U.S.-Mexico border as an American problem.

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López Obrador’s willingness to take on the burden of housing the migrants — perhaps for extended periods — is a surprising development, especially since he campaigned as a progressive and has criticized Trump.

“The medium- and long-term solution is that people don’t migrate,” said Olga Sánchez Cordero, Mexico’s incoming interior minister. “Mexico has open arms and everything, but imagine, one caravan after another after another, that would also be a problem for us.”